Depth estimations in uncharted rivers would enable safe navigation and flood hazard predictions. Radar and optical instruments and techniques have been developed to remotely measure water depth but are typically of limited use in deep or turbid river waters where significant attenuation and scattering of the electromagnetic signal occurs. There is also an indirect approach that estimates river depth based on the local hydrodynamic relationship between the steady currents in simple one-layer shallow flows and the depth. This inverse hydrodynamic approach requires measurements of the surface velocity field and/or elevation, and the estimation of other model parameters such as the discharge and the bottom friction. Several image-tracking techniques have now been developed that are capable of determining surface currents with 10-30 m spatial resolution from airborne infrared imagery or satellite-borne multispectral imagery. Additionally, global observations of water surface elevation with an estimated 100 m resolution and 1 cm vertical accuracy are anticipated from the planned NASA's Surface Water and Ocean Topography (SWOT) altimeter.